Rosa, who is also making a shirt-stripe boxes quilt, has asked me how I quilted mine. I did exactly as Kaffe Fassett suggested and machine quilted in the ditch of each cross within the boxes.
As I have already mentioned, my corners did not match very well so this method was slow as I could not stitch continuous lines and had to do each box individually.
On the back of the quilt I used a plain blue fabric as I thought there was quite enough happening on the front of the quilt.
Actually, I used a piece of sheeting fabric and I have since read that you should NEVER use sheeting fabric on the back of quilts as it is more tightly woven than quilting fabric and harder to quilt. Because I machine quilted I didn't find it to be a problem, but I will remember this for the future.
Good luck with your quilt Rosa.